Question: $\dfrac{ 10n - 7p }{ -8 } = \dfrac{ 9n + 2q }{ 4 }$ Solve for $n$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ 10n - 7p }{ -{8} } = \dfrac{ 9n + 2q }{ 4 }$ $-{8} \cdot \dfrac{ 10n - 7p }{ -{8} } = -{8} \cdot \dfrac{ 9n + 2q }{ 4 }$ $10n - 7p = -{8} \cdot \dfrac { 9n + 2q }{ 4 }$ Reduce the right side. $10n - 7p = -{8} \cdot \dfrac{ 9n + 2q }{ {4} }$ $10n - 7p = -{2} \cdot \left( 9n + 2q \right)$ Distribute the right side $10n - 7p = -{2} \cdot \left( {9n} + {2q} \right)$ $10n - 7p = -{18}n - {4}q$ Combine $n$ terms on the left. ${10n} - 7p = -{18n} - 4q$ ${28n} - 7p = -4q$ Move the $p$ term to the right. $28n - {7p} = -4q$ $28n = -4q + {7p}$ Isolate $n$ by dividing both sides by its coefficient. ${28}n = -4q + 7p$ $n = \dfrac{ -4q + 7p }{ {28} }$